The inverse Laplace transform of the function is 1 + et 1 - et 1 + e-t 1 - e-t

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Question
The inverse Laplace transform of the function is
Options
A. 1 + e^t
B. 1 - e^t
C. 1 + e^-t
D. 1 - e^-t

Correct Answer

1 - e^-t

Process Control and Instrumentation problems

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2. The offset introduced by proportional controller with gain K_cin response of first order system can be reduced by
Options
A. reducing value of K_c.
B. introducing integral control.
C. introducing derivative control.
D. none of the above.

4. In a second order under damped system, the
Options
A. time required for the response of first reach its ultimate value is called the response time.
B. overshoot (which is a measure of how much the response exceeds the ultimate value) increase with the decrease of damping co-efficient e.
C. decay ratio (which is the ratio of the sizes of successive peaks) is equal to the reciprocal of overshoot.
D. characteristics of a step response is represented by

5. The time constant of a unity gain, first order plus time delay process is 5 min. If the phase lag at a frequency of 0.2 rad/min is 60�, then the dead time (in minutes) is
Options
A. 5?/12
B. ?/6
C. ?/12
D. ?/3

9. Water is entering a storage tank at a temperature T₀ and flow rate Q₀ and leaving at a flow rate Q and temperature T. There are negligible heat losses in the tank. The area of cross-section of the tank is A₀. The model that describes the dynamic variation of temperature of water in the tank with time is given as :
Options
A. Q₀(T₀ - T) = A_c .
B. Q₀T₀ - QT = A_c .
C. Q(T₀ - T) = A_c .
D. Q(T₀ - T) = A_c .

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